looking for a solution for an optimization problem

hi, I am looking for a solution for an optimization problem,

I have a set of non-linear equations and I am looking for positive results, what is the method to follow? an example if possible.

thanks a lot

Answer 1

[Alan Weiss]

You might find this example relevant. If you have a recent MATLAB version, then look at this example.

Alan Weiss

MATLAB mathematical toolbox documentation

[Zinedine Gueddal]

Thanks, excuse me because I’m a beginner, for exemple: If i look for solving this 3 equations: (X(1)^2)-1=0; (x(2)^2)-4=0; (x(3)^2)-9=0; and i have contrainte: X(1:3)>=0; I maked program:confuneq.m: Function [c, ceq] =confuneq(x) c=-x(1:3); ceq=(X(1)^2)-1=0 (x(2)^2)-4=0 (x(3)^2)-9=0; And exemple.m: X0=[0,0,0]; options=optimoptions('lsqnonlin',FiniteDifferenceType',central'); X=lsqnonlin(@confuneq, x0, [], [], options); The x result [0 0 0]! Spite not satisfate [1 2 3] result why?

[Alan Weiss]

The problem is your initial point has gradient 0. Take almost any nonzero initial point.

Alan Weiss

MATLAB mathematical toolbox documentation

[Zinedine Gueddal]

Thanks a lot, is there an other program using fmincon for solving this?

[Zinedine Gueddal]

I changed the initial value for x0 =[0. 1,0.1,0.1] but the result x =[9.8900e-16,0.1,0.1] not [1 2 3], can you help me please

Answer 2

[Alan Weiss]

I think that you need to be more careful when trying to follow the example. EITHER use fmincon OR use lsqnonlin, not both. The fmincon workflow:

fun = @(x)0;

The nonlinear constraint function is nlcon at the end of this example.

Set lower bounds of zero.

lb = zeros(3,1);

Run fmincon starting from [0.1;0.1;0.1];

x0 = 0.1*ones(3,1);
[x,fval,eflag] = fmincon(fun,x0,[],[],[],[],lb,[],@nlcon)

This finds the solution you want.

Alan Weiss

MATLAB mathematical toolbox documentation

function [c,ceq] = nlcon(x)
c = [];
ceq = [x(1)^2 - 1;
    x(2)^2 - 4;
    x(3)^2 - 9];
end

Answer 3

[Zinedine Gueddal]

Thank you very much, it is for the first time I see this excellent idea (flag instead of exitflag)!

Answer 4

[Zinedine Gueddal]

I tried this program for fmincon on its market and I found positive results, but I tried another program but I found results at x near zero, how can I find x and not negative ?

[Alan Weiss]

I'm sorry, but I do not understand what you are asking. Are you saying that different input data yields different results, and some of those results are not satisfactory? Or are you saying that you tried running another program and it gave better results? Or are you asking something else?

Alan Weiss

MATLAB mathematical toolbox documentation